MinT - Best Known (94, 94+41, s)-Nets in Base 3

Best Known (94, 94+41, s)-Nets in Base 3

(94, 94+41, 192)-Net over F₃ — Constructive and digital

Digital (94, 135, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 45, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(94, 94+41, 306)-Net over F₃ — Digital

Digital (94, 135, 306)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+41, 6511)-Net in Base 3 — Upper bound on s

There is no (94, 135, 6512)-net in base 3, because

1 times m-reduction [i] would yield (94, 134, 6512)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8604 023233 328791 420040 931369 600904 638796 429996 840129 616313 070209 > 3¹³⁴ [i]